Question 978428
If the information given was {{{system(tan(x)=1,cos(x)=-sqrt(2)/2)}}} ,
that is more information than needed. Very generous!
{{{system(tan(x)=1,cos(x)<0)}}} would have been enough information.


{{{system(tan(x)=1,tan(x)=sin(x)/cos(x))}}} ---> {{{sin(x)/cos(x)=1}}} ---> {{{sin(x)=cos(x)}}} .
So {{{highlight(sin(x)=cos(x)=-sqrt(2)/2)}}} gives you 2 of the trigonometric functions.
{{{system(sec(x)=1/cos(x),cos(x)=-sqrt(2)/2)}}} ---> {{{sec(x)}}}={{{1/((-sqrt(2)/2))}}}={{{-1(2/sqrt(2))}}} ---> {{{sec(x)=-sqrt(2)}}} and
{{{system(csc(x)= 1/sin(x),sin(x)=cos(x))}}} ---> {{{csc(x)=1/cos(x)=-sqrt(2)}}} too.
So {{{highlight(sec(x)=csc(x)=-sqrt(2))}}} gives you another 2 trigonometric functions.
Finally, {{{system(tan(x)=1,cot(x)=1/tan(x))}}} ---> {{{cot(x)=1/1=1}}} ,
so {{{highlight(tan(x)=cot(x)=1)}}} completes the set of 6 trigonometric funcions,
and as a bonus {{{x=45^o+180^o=225^o}}} ,
or if you want the angle in radians, {{{x=pi/4+pi=5pi/4}}} ,
because {{{sin(y)=cos(y)=sqrt(2)/2}}} for the reference angle {{{y=45^o}}} or {{{y=pi/4}}} .